A sememe is defined as the minimum semantic unit of human languages. Sememe knowledge bases (KBs), which contain words annotated with sememes, have been successfully applied to many NLP tasks. However, existing sememe KBs are built on only a few languages, which hinders their widespread utilization. To address the issue, we propose to build a unified sememe KB for multiple languages based on BabelNet, a multilingual encyclopedic dictionary. We first build a dataset serving as the seed of the multilingual sememe KB. It manually annotates sememes for over 15 thousand synsets (the entries of BabelNet). Then, we present a novel task of automatic sememe prediction for synsets, aiming to expand the seed dataset into a usable KB. We also propose two simple and effective models, which exploit different information of synsets. Finally, we conduct quantitative and qualitative analyses to explore important factors and difficulties in the task. All the source code and data of this work can be obtained on https://github.com/thunlp/BabelNet-Sememe-Prediction.